Yes, the slider tools that allow you to rotate and tilt he view work correctly for the given date. Keep in mind that orbits of different objects are in different planes, and when projectde onto a 2-D computer screen it may be hard to visualize exactly what it's doing. The tilt & rotate tools allow you to get a better idea of an orbit's inclination relative to the Earth's orbit or other planets.
As an example I've attached a couple of screen shots of Eros 433's orbit and current position as viewed from different angles for today, March 1. Note that even though the views are tilted and rotated, Eros's position relative to the planets is the same for each view. The source web page is here:
JPL Small-Body Database Browser
Another set of tools to experiment with on that page are the player buttons, similar to what you use on a video player, which allows you to see the orbits sped up. Click on the >> button and it moves pretty quickly - you get a sense of how objects near the sun move much faster than tgose further away.